Calculate the mean and standard deviation of the number of hours cars are parked in the lot. When parking a car in a downtown parking lot, drivers pay according tothe number of hours or parts thereof. The probability distribution of the number of hours cars are parked has been estimated as follows. x      1      2     3     4     5     6     7     8 p(x) .24  .18  .13   .10  .07  .04  .04  .20   The cost of parking is $2.50 per hour.

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The probability distribution of the number of hours cars are parked has been estimated as follows.

x      1      2     3     4     5     6     7     8

p(x) .24  .18  .13   .10  .07  .04  .04  .20

The mean is equal to:

1*0.24 + 2*0.18 + 3*0.13 + 4*0.1 + 5*0.07 + 6*0.04 + 7*0.04 + 8*0.2 = 3.86

The standard deviation is:

sqrt((1^2*0.24 + 2^2*0.18 + 3^2*0.13 + 4^2*0.1 + 5^2*0.07 + 6^2*0.04 + 7^2*0.04 + 8^2*0.2) - 3.86^2)

=> sqrt((1*0.24 + 4*0.18 + 9*0.13 + 16*0.1 + 25*0.07 + 36*0.04 + 49*0.04 + 64*0.2) - 3.86^2)

=> sqrt(21.68 - 14.8996)

=> sqrt(6.7804)

=> 2.60392

The mean of the probability distribution is 3.86 and the standard deviation is approximately 2.60392

Approved by eNotes Editorial Team
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